Alzheimer's Disease (AD) and other dementias affect approximately 25 million people worldwide, taking a huge toll on the physical and psychological well being of elderly patients. A major reason for lack of progress in AD treatment is a fundamental lack of understanding regarding its cause and mechanism of progression. Despite impressive progress in detecting and quantifying disease progression in AD using sophisticated neuroanatomic algorithms, there are very few system-level models which can explain the observed patterns of neurodegeneration in AD. We now propose a novel model of atrophy as a diffusion process on a hypothesized brain network. The model mathematically encodes the basic understanding that propagation follows fiber pathways, going from more to less atrophied regions at an outward rate proportional to the local atrophy gradient, in a manner akin to heat transfer in a network with temperature gradients. Surprisingly, the model implies atrophy patterns in AD and other degenerative diseases. Finally, we propose to use our model to predict the future atrophic patterns for any patient using their baseline neuroimaging data.